Transformer system



Nv. 10, 1942. H. w. BoDE- 2,301,245

TRANISFQRMER SYSTEM l v Filed Aug. 13, 1940 3 Sheets-Sheet 1 i W2 j l 75 593 1 I I Tn BVM/Mm ATTORNEY N0v.1o,1942. w, BODE I 2,301,245

TRANSFORMER SYSTEM Filed Aug. 13, 1940'y ssheets-sheet 2 /Nvwron HM. BODE Hyg/M ATTORNEY Nov. 1o, 1942.

H. w. BQDE TRANsFoRuEn SYSTEM s sheets-sheet s Filed Aug. 13, 1940 INI/E N TOR H. nf 500E Patented Nov. 10, 1942 UNITED STATES PATE NT OFFICE- 'raANsFonMEa SYSTEM Application August 1.3, 1940, Serial No. 352,422

6 Claims.

This invention relates to transformers and more particularly to multiple transformer systems for the transmission of currentsl of all fre-h-V quencies in a continuous wide range. Its principal objects are to improve the phase shift characteristics of multiple transformer systems and to increase the frequency range in which uniform transmission may be accomplished.

The image or video currents in a television system, for example, may range in frequency from a few cycles per second to several million. Faithful reproduction of the visual image requires that these currents be transmitted at all frequencies Without variation of their amplitude relationships and .without change of their relative phases.

This imposes'severe requirements on the attenuation and phase shift characteristics of any transformer that may be used to increase or decrease the voltages of the currents and, in particular, requires a high degree of linearity in the phase shift characteristic, since image distortions re-4 sulting from any departure from linearity are very readily perceived by the eye. Y

Systems of the type contemplated by the invention comprise a plurality of tuned transformers connected to providev a corresponding number of parallel transmission paths between com- -mon input and common output terminals and so proportioned that each operates efficiently in a separate part of the whole frequency range. I have found that, in general, the existence of parallel transmission paths may give rise to excessive and irregular phaseshifts and that, when the parallel paths are constituted by transformers, the winding inductances are particularly troublesome sources of phase shift irregularities.

In accordance with the invention, improved transmission characteristics are obtained by organizing and proportioning the elements of the several paths in such manner that the phase shift produced by the complete transformer system is substantially the minimum consistent with the attenuation characteristic and so that the attenuation is substantially constant at all frequencies in the operating range, The term minimum phase shift as applied to networks is dened in my earlier Patent 2,123,178, issued June 12, 1938, wherein it is shown that for any prescribed attenuation characteristic the minimum possible phase shift is uniquely determined by the variation of the attenuation with frequency. Networks realizing this minimum phase shift characteristic have been called minimum phase shift networks. The conditions of minimum -phase shift and uniform attenuation are achieved substantially in the systems of the invention by tuning certain effective inductances of the several transformers in a manner described hereinafter and by the inclusion of suitably proportioned resistances in each of the transmission paths.

vA feature of the invention is that the uniformity of the attenuation and the minimum phase shift characteristic are independent of the values of the terminal impedances to which the transformer systems may be connected. Another feature is the substantially pure resistance character of the several-short circuit and open `circuit driving point and transfer impedances of the system.

These and other features of the invention will be more fully understood from the detailed description .which follows and by reference to the accompanying drawings, of which:

Fig. 1 represents one form of the invention;

Figs. 2, 3, 4.and 5 are diagrams used in the explanation of the principles of the invention;

Fig. 6 represents a second form of the invention;

Figs. 7 and 8 are diagrams explanatory of Fig. 6;

Figs. 9, 10 and 11 illustrate a third form of the invention; Y

Figs. 12, 13 and 14 illustrate a fourth form of the invention;

Fig. l5 represents a modification of the invention for extending the frequency range of operation; and f Fig. 16 represents another modification for the same purpose.

The transformer system shown in Fig. 1 is of a type suitable for stepping up the vvoltage from a low impedance source connected to terminals I I' and delivering the increased voltage to a high impedance load connected to terminals 2, 2 It comprises three separate shielded transformers T1, T2 and T3 the secondary windings of which are connected in series between the output terminals and the primary circuits of which are connected in parallel atthe input terminals. All of the transformers have the same transformation ratio, designated by and all have theirv windings poled in the same Way. Grounded shields, which are indicated by the dotted lines between the transformer windings, serve to eliminate any electrostatic coupling between the pri- Aby tuning condensers included in circuit with each transformer the capacities of which are suitably proportioned with respect to the leakage and mutual inductances of the windings. In the figure the designations of the condensers represent their capacities. Transformer T1 is tuned .by a capacity C14-r2 in shunt to the secondary winding which resonates with the effective leakthe system as a minimum phase i produce the desired age inductance at a preassigned frequency. The mutual inductance of the windings is made sufl'lciently great to provide efcient transmission at l `this transformer is also madesufficiently great to have negligible eiect on the transmission throughout the operating range, in which case the transformer and condenser combination may be treated as a simple resonant circuit. The path including transformer T3 is the same as the middle path in conguration but in this case the windings are of low inductance and are so proportioned that the capacity C3 resonates, with the effective mutual inductance at the preassigned frequency. The leakage inductance is made sufciently small so `that its effect is negligible at any frequency in the operating range, thus reducing the network effectively to a highpass filter. ,l I

The control of the phase shift and attenuation characteristics is effected by means of suitably proportioned resistances, designated as Ruiz, Rei and Rei, connected in shunt to the several paths across the secondary windings cf the transformers. The presence of these resistancs in the circuit permits the construction of shift network. By suitably proportioning their values in relation to each other and to the inductances and capacities of the system, substantially uniform attenuation and zero phase shift can be attained.

The relationship of the element values which characteristics will now be developed. vFor this purpose the circuit diagram may be simplified by substituting for each of the transformers an equivalent network of the type shown in Fig. 2 which is the' equivalent of a.

transformer having a primary inductance P, a secondary inductance S, and a .mutual inductance M. The series and shunt inductances rep-- resent respectively the total effective leakage inductance and the effective mutual inductance, both referred to the primary circuit. These inductances may be described-as parasitic vinductances, since they represent undesiredI but unavoidable reactances and susceptances which absorb part of the energy of the oscillations inipressed on the transformer and cause its performance to depart from that of its ideal prototype. The reactance of the leakage inductance absorbs part of the impressed voltage and the susceptance of the mutual inductance absorbs part of the current supplied to the transformer.

The application of. the equivalence ltheorem Vto the network of Fig. 1 produces the simplified system of 3 when the mutual inductances of transformers T1 and T2 and the leakage inductance of Ta are disregarded. The resistances and the capacity C1 have all been transferred to the primary sides of the ideal -transformers with appropriate changes in their values indicated by the removal of the impedance transformation factor Q.

The relationships of the element values may be determined by computing certain of the open circuit or short-circuit characteristics ofthe net- Iwork'and subjecting these to particular conditions consistent with the desired characteristics ofthe system. For the system of Figs. 1 and 3 it is convenient to compute first the open circuit voltage at terminals 2, 2' in response to a voltage applied' to terminals l, l'. This is evidently equal to the sum of the separate voltages across resistances R1, R2 and R3 multiplied by the common transformationratio i If the voltage at terminals l, l be denoted by V1 and the voltages 4across R1, Rr and Ra by e1, e2 and e3, respectively, it is readily shown that:

Where p denotes the quantity iw, u being the pulsatance or 2f times frequency. If the element values are subject to the relationships 2 1 -lalii-l,

w., wo

which is equal to unity and independent of frequency. The quantity a appearing in Equations 5 and 6 is a simple numeric, the value of which is so far undetermined. Under the conditions of Equations 4 and 5, the open circuit voltage V2 at terminals 2, 2 is given by Since there are nine impedance elements in the system, aside from the ideal transformers,

-the relationships of Equations 4 and 'are insufficient for the complete determination of the network. They do, however, suffice to establish the minimum phase` shift character of the system as may be seen from the following considerations.

A general transmission equivalent of the complete system of Fig. 3 comprising a T-network and a single ideal transformer is shown in Fig. 4. The symbolsr Zio. Zzo and Zu represent respecy tively the primary open circuit impedance, the

secondary open circuit impedance andthe open circuit transfer impedance. The transformation factor I appearing in the designations refers the impedance values t0 the primary side of the system. Equations 6 and 7 show that, as a result of the relationships of the element values, the ratio'of the open circuit output voltage to the impressed voltage is constant and equal to -I Examination of Fig. 4 shows that the voltage ratio is also equal to Zu-z-Zio.- It follows then, that Zu= I Zi (8) Since Zie, the primary opencircuit impedance, is

Zzo/d-Zu/i becomes equal to the secondary .short-circuit impedance, referred of course to the primary side, and is therefore also physically realizable. The fact that the system of Fig..3 is

' equivalent to a ladder type network of real elements is sufcient to establish its minimum phase shift character as pointed out in' my earlier Patent 2,123,178 of June 12, 1933. This result has been made possible by the inclusion of the resistance elements in the several transmission paths.

Equations 4 and 5 provide five independent relationships of the nine impedance coemcients of the system, the quantity a being undetermined, leaving three relationships to be imposed for the complete determination of the network proportions. In accordance with the invention, the additional relationships are such as to make the constancy of the voltage ratio 4independent of the magnitudes of the impedances between which the network is connected. This is accomplished by proportioning the relative values of the co-rresponding elements in the different paths so that the primary open circuit impedance, and

therefore the open circuit transfer impedance,

and the secondary short-circuit impedance become purely resistive. then equivalent to a simple resistance pad together with an ideal transformer.

The primary open circuit impedance is given by Zlo=Rl RI 7) and the secondary short-circuit impedance, Zzc,

These become respectively equal to Ri and Rz when .4

and

`which together with- Equations 4 and 5 serve to determine completely the proportions of the network elements. The values of the inductances The network of Fig. 3 is :2.

and capacities are given below inv terms of R1 and we, which may be assigned arbitrarily.

When given the proportions indicated by the above equations, the network of Fig. 3 becomes exactly equivalent to that o-f Fig. 5 which comprises a single shunt resistance of value R1, a

single series resistance equal to 2Ri and an ideal transformer. Its phase shift is zero at all fref quencies and the attenuation is constant when connected between resistive terminal impedances i of any values. The three paths have respectively low-pass, band-pass, and high-pass transmission characteristics, the band of the middle path being, in general, relatively narrow and serving principally to sustain thev transmission at the region of the common cut-off frequency of the low-pass and high-pass paths.

-Since the circuitof Fig. 3 has been derived from that of Fig. l on the assumption that one of the parasitic inductances of each'transformer may be disregarded, the system of Fig-1 will not behave exactly as indicated by the equations, but will realize the results to a close degree of approximation. The susceptance of the mutual inductance of transformer T1 sets a low frequency limit to the range of uniform transmission and the leakage inductance of transformer Ta operates to establish a high frequency limit. By using transformers having magnetic cores of high permeability material, such as the alloys of iron and nickel disclosed in U. 4S. Patents 1,586,884, June 1, 1926, and 1,768,443, June 24, 1930, lboth to G. W. Elmen, the effects of these parasitic inductances may be made negligibly small in a frequency range extending from a lower limit of less than twenty cycles per second to an upper limit greater l than three million cycles per second.

The modified form of the invention shown in Fig. 6 differs from that of Fig'. 1 in the disposition of the resistance elements in the circuit and in the tuning of 'the band-pass transformer T2. The resistance elements are connected in the primary circuit as series impedances and the mutual inductance of transformer Tz is tuned by a condenser connected in shunt in the secondary circuit. This transformer has a relatively low mutual inductance and should have negligibly small leakage. As in the system of Fig. 1, all of the transformers have the same transformation ratio and are tuned by their associated condensers to the same resonance frequency.

The equivalent network is shown in Fig. 7, the mutual inductance of transformer Ti and the leakage inductances of T2 and T3 being disregarded. The impedance coemcients of the significant elementsin the low-pass path are denoted by R, L and C, the subscripts being dropped as unnecessary. The values of the corresponding elements in the other paths necessary for the realization of the desired characteristics are indicated inthe figure in terms of the low-pass element values. The corresponding elements in the high-pass and low-pass paths have the sarne values while in the band-pass path the values are modified by the factor two.

These proportions may be established by la procedure similar to that'followed in connection with Figs. 1 and 3. The voltage transfer ratio with the secondary terminals open is readily computed as the sum of the transfer ratios for the individual paths. Setting this equal to the transformation ratio of the transformers fixes the condition that vthe open circuit transfer impedance must be equal to the primary open circuit impedance or, in other words, that the equivalent T-network corresponding to Fig. 4 has its lefthand series impedance equal to zero and therefore reduces to a simple L-network. As in the ca se of Fig. 3, the right-hand` series impedance of the equivalent`T-network becomes equal to. the secondary short-circuit impedance referred to the primary side of the ideal transformer. The further step of making the primary open circuit impedance and the secondary short-circuit impedance both purely resistive leads to the proportions indicated and to values of L and C in terms of the resistance R and the common resonance frequency as follows:

,en wo :Zwak A third form of the invention shown in Fig. 9 is characterized by the parallel connection of the three paths at both primary and secondary terminals. In the preceding formsI where the circuits are connected in parallel on one side and in series on the other, the three-element networks constituted by the significant impedances of each path have the configurations of L-networks with the series branches on the same side as the parallel connections and the shunt branches on the same side as the series connections. This is in accordance with a common practice in the connection of multiple lter systems. n the system of Fig. 9, since the circuits are connected in parallel at both terminals, the individual networksV in each path have series terminations at both ends. The significant elements of the high-pass and low-pass paths form T-networks and those of the middle path form a simple series circuit.

' For the realization of the desired characteristics the transformer T2 in the middle or band-pass path is required to have a transformation ratio equal to one half that of the. other two transformers. Its significant inductance is the leak- .age inductance, the mutual inductance being made sufiiciently large to offer a negligibly small shunt susceptance. As in the case of the preceding systems, the mutual inductance of T1 and the leakage inductance of T3 are assumed to have negligibly small effects on the characteristics in the operating range.

The relative values of the elements may be established by a. procedure similar to that followed in the preceding examples, but differing therefrom in detail. Tobegin with the transformation ratio of transformer T2 may be leftundetermined. The primary short-circuit transfer admittance and the primary short-circuit input admittance may be computedreadily and by setting these respectively equal to 1+d1R, and l-z-R, respectively, it turns out that the effective mutual impedance must be equal to the secondary open circuit impedance, both referred to the primary circuit, and hence must be physically realizable. This suffices to establish the minimum phase shift character of the system. A further consequence is that the equivalent T-network of the whole system reduces to an L -network of the configuration shown in Fig. 11. The voltage transfer ratio from the secondary terminals on open circuit also beratio i. Certain relationships of the circuit elements are likewise fixed, but not sufficient for the complete determination of their proportions. Computing the secondary short-circuit input admittance and setting its value equal to 1-:-R i 2 establishes the ratio of the transformer T2 as one half that of the others and reduces the transmission equivalent of the system to the purely resistive system of Fig. l1.

The condition of constancy of the-open circuit voltage transfer ratio might have been applied as in the preceding examples, but the computation of this ratio is rather complex, consequently the indirect method indicated above is preferable.

The modification shown in Fig. l2 is characterized by the series connection of the several paths at both the primary Transformer T2 has a transformation ratio twice as great as that of the other transformers and is tuned bya shunt condenser C2 which resonates with the effective mutual inductance. Transformers Ti and T3 are similar to the corresponding transformers in the other figures. The equivaient network is shown in Fig. 13 with the proportions. of the element coefficients indicated by their designations. proportions to provide the desired characteristics is most conveniently effected by computations of the primary open circuit transfer impedance, and the primary and secondary open pedances. The transmission equivalent of Fig. 13 is shown in Fig. 14.

The principal factors which limit the operating frequency range of transformer systems are the leakage inductance of the high frequency transformers and the mutual inductance of the low frequency transformers. The former gives rise to a high frequency limit and the latter to a low frequency limit to the range of substantially uniform transmission. The self-capacities of the transformer windings also tend to limit the transmission range, their principal effect being to sharpen the cut-off at the upper frequency limit of the operating range. The capacity which is mainly effective in this is that of the high impedance winding of the high frequency transformer. The winding capacities ofthe low frequency transformer are absorbed in the'capacity of the tuning condenser and those of the intermediate transformer have substantially no effect since this transformer contributes to the transmission of the system only in a narrow frequency range.

For most purposes the three-transformer systems provide adequately wide transmission bands, but a substantial addition to the frequency range may be obtained by an extension of the principle already discussed to systems including larger numbers of transformers. Such a system comprising five transformers is illustrated in Fig. 15. The lower part of the gure. enclosed by broken lines, represents a three-transformer group like that of Fig. 1, but including an additional ca.- pacity Caf connected across the secondary terminals of transformerTa. "This capacity may be the self-capacity of the may include that of an added condenser. Additional transformers T4 and T5, .tuned -by condensers C4 and Cs and having associated resistances R4 and Rr,` areprovided to extend the operating range to higher frequencies, the two together with the lower group constituting in effect a three-transformer group also like that of cornes constant and equal to the transformation '15 Fig. 1.

At the upm and secondary terminals.

The establishment of theA circuit input iml secondary Winding or it f limitof its operating range the I Figs. 6, 9 and 12 may also the type shown series resistance.

proportioned to resonate with .resonate with the effective lower group behaves like a low-pass lter having a cut-olf frequency determined by the leakage inductance of transformer T: and the shunt ca pacity C1. All of the other elements of this group have substantially no effect at the upper frequency limit and may'therefore be ignored. Transformer T4,

quency, and transformer T5, the mutual inductance of which is likewise Vtuned by capacity C5, provide respectively intermediate and high-pass paths coordinated in the manner already descrlbedwith the low-pass path provided by transformers Ti, T2 and Ta. Resistances R4 and vRe are equal and have the same value as those of lthe lower group. The winding inductances of T4 `and Ts and their respective tuning capacities have values related to the resistances and the new cut-oil frequency in accordance with Equation 13. 4Similar extensions of the systems of be made.

Another way of extending the frequency range is illustrated in Fig. 16 as applied to a system of leakage inductance of the high frequency tra-nsformer is diminished by means of a small compensating capacity Ca' connected in shunt to the As is well known, the eifecvtive reactance of a tion of this typeis the same tive inductance for a considerable range of frequencies above zero. By the proper choice of the capacity Ca it is therefore possible to annui all or part of the effect of the transformer leakage inductance in the `whole operating range of the system. The value of the -shunted resistance -should be increased somewhat so that the eilective resistance of the combination may have the correct value in the high frequency range. The

same method of compensation may be applied to the intermediate frequency path as shown, a1- thoush in this case it is less necessary. In the low frequency path the shunting eil'ect of the transformer mutual sated to some extent by shunting the series resistance by a relatively large inductance. At low frequencies the inductance becomes the dominant part of the impedance and the voltage impressed on the system tends to divide between this series 'branch and the transformer in proportion to their inductances. 'The added inductance-L1' may be proportioned to maintain approximately the same output voltage as obtains at higher frequencies.

What is claimed is:

1. A transformer system comprising a plurality of transformers connected .to provide parallel transmission paths between two pairs of terminals', each of said transformers having closely coupled windings, a condenser connected in shunt to a winding of a first of said transformers and the effective leakageinductance of thev transformer at a prealsig'ned frequency whereby the transmission d thetransformer is limited substantially to frequencies below said assigned frequency, a condenser connected in series with a winding of a second of said transformers and proportioned to resistance-capacity combinaas that vof a negainductance may be compenthe leakage inductance of which. is tuned by capacity C4 to the new cut-olf fresaid second transformer at said preassigned frequency, whereby the transmission range of said second transformer is limited substantially to frequencies above said preasslgned frequency, a condenser connected in circuit with said third transformer, and resistors included in circuit with each of said transformersrespectively, said thirdv transformer being tuned by its'associatedcondenser to provide tron ina narrow frequency range centered at assigned frequency and said resistors having resistance values proportionedwith respect to the transformer inductances and the` capacities of the said condensers to provide uniform attenuation and minimum phase shift for transmission in a wide range of frequencies above and below said preassigned frequency.

in Fig. 6. Here the eect of the 2. A system in accordance witlrclam 1 charthe primary circuits of the transformers in parallel and the connection of the secondary circuits in series.

3. A system in accordance with lclaim 1 in which the effective mutual inductance of the said second transformer is equal to the effective leakage inductance of the said ilrst transformer.

4. A system in accordance with claim l in which the effective mutual inductance of the said second transformer is equal to the eiective leakage inductance of the said' first transformer and in which the said third transformer is tuned by a condenser in shunt to one ofits windings and has an effective mutual inductance equal to twice the effective leakage inductance of the said rst transformer.

5. A system in accordance with claim 1 in which the said third transformer is tuned by a series condenser having a capacity which resonates with the effective leakage inductance of the transformer at the said preassigned frequency and in which the effective leakage inductance of the said third transformer is equal to one vhalf the effective leakage inductance of the said'rst transformer.

6. A transformer system for currents of a wide range of frequencies comprising a group of three each of said transformers, said condensers and resistors having capacity and resistance values proportioned with respect to the inductances of said transformer such that the open circuit output voltages of the several paths in response to mutual inductance of an oscillation input of constant amplitude are substantially in the proportions quency function '1++'(.1;)'

W.' BODE.

relatively said pre- 

